Axion inflation in type II string theory

Inflationary models driven by a large number of axion fields are discussed in the context of type IIB compactifications with N=1 supersymmetry. The inflatons arise as the scalar modes of the R-R two-forms evaluated on vanishing two-cycles in the compact geometry. The vanishing cycles are resolved by small two-volumes or NS-NS B fields which sit together with the inflatons in the same supermultiplets. String world sheets wrapping the vanishing cycles correct the metric of the R-R inflatons. They can help to generate kinetic terms close to the Planck scale and a mass hierarchy between the axions and their nonaxionic partners during inflation. At small string coupling, D-brane corrections are subleading in the metric of the R-R inflatons. However, an axion potential can be generated by D1 instantons or gaugino condensates on D5-branes. Models with a sufficiently large number of axions admit regions of chaotic inflation which can stretch over the whole axion field range for potentials from gaugino condensates. These models could allow for a possibly detectable amount of gravitational waves with tensor to scalar ratio as high as r<0. 14.